Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C7 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×C7×#157 |
| Fitting, socle | C2×C33×C7 ⋊ C4 |
| derived | C32 ⋊ C2×C3×C4×C7 |
| Hall | C33×C7 ⋊ C2×C4 |
| Sylow | C33 ⋊ C2×C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | #157 |
| commutator, hypocenter | C32 | C2×C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33×C7 | C4 |
| prime radical | C2×C3×C7×C3⋊D3 | C2 |
| cosocle | C3⋊D3 | C22×C3×C7 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C3×C7 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 863);